Problem 1: (15 pts) The proprietor of a clothing store in New York wants to study the average age of his customers. A random sample of 25 customers revealed an average age of 35 years with a standard deviation of 5 years. a) (2 pts) What is the point estimate of the true average age of all customers? b) (8 pts) Construct 90% confidence interval (interval estimate) for the true average age of all customers. (c) (5 pts) Interpret the meaning of the interval you computed in part (b).erent Problem 2: (25 pts) An operations manager for American Airlines wants to determine the percentage of passengers who prefer aisle seats. A survey suggests 42% of air passengers prefer an aisle seat. The survey results are based on a 3M Privacy Filter survey of 275 air passengers. a) (2 pts) What is the point estimate of the true proportion of passengers who prefer aisle seats? b) (8 pts) Construct 99% confidence interval (interval estimate) for the true proportion of passengers who prefer aisle seats. orized (b) (8 pom c) The manager wants to test whether the true proportion of passengers who prefer aisle seats is significantly greater than 38%. i. (4 pts) Set up the null and the alternative hypotheses related to the study. ii. (5 pts) State the appropriate test statistic and its distribution.iii. (4 pts) Compute the test statistic. iv. (2 pts) At a = 0.05 level of significance, test whether the true proportion of passengers who prefer aisle seats is significantly greater than 25%. Problem 3: (20 pts) Suppose that the cholesterol level of women at ages 20-29 is normally distributed with a mean of 172 (in mg/dL) and standard deviation of 32.2 (in mg/dL). Suppose 20 women at ages 20-29 are selected at random. Let X be the mean cholesterol level of a sample of 16 women at ages 20-29. (a) (8 pts) Determine the mean and the standard deviation of the sampling distribution of X. (b) (2 pts) Circle the correct answer: Sampling distribution of X is a (Normal / Approximately Normal) distribution.en diferentes ente (c) (10 pts) Find the probability that the sample mean cholesterol level is more than 175 (mg/dL). Problem 4: (25 pts) According a study, 12% of U.S. adults with online services currently read e-books. Assume that this percentage is true for the current population of U.S. adults with online services. A random sample of 750 adults with online services is selected. Let X be the number of adults who read e-books out of those 600 adults. (a) (5 points) Is X a binomial random variable? If "Yes", identify n and p. (b) (8 points) Compute the mean and standard deviation of X. di) SVI lo nsom s die (c) (4 points) Check whether the Normal approximation to Binomial distribution is appropriate in this study. To nobudiggity galkomen (d) (8 points) What is the approximated probability that number of adults who read e-books is at most 100